The group, known as the Green Brigade, had already been banned from receiving away tickets or games.
Now, the club have decided to take their season tickets at Celtic Park away too.
According to the BBC, Celtic made the decision due to what they deem as the group's consistent failure to adhere to club and stadium rules.
The fan group, which reside in the north curve of Celtic Park, typically organise a tifo for games.
The club asked its fans not to bring in any banners relating to the ongoing conflict between Israel and Hamas.
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The Green Brigade and other Celtic fans defied the request, though, starting with their Champions League 2-2 draw with Atletico Madrid.
Numerous Palestine flags were spotted around the ground with the Green Brigade handing out Palestine flags before the game and forming a display of their own.
In a statement before the European clash, the Green Brigade said the ban from the club was 'motivated by a desire to quash political expression within the Celtic support'.
It also accused the Celtic board of being disingenuous and hypocritical, citing issues over the club's history and the war in Ukraine.
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Celtic are expected to receive a fine from UEFA for the displays shown at the game.
Their next outing sees them take on St Mirren at home on Wednesday night with the Hoops five points ahead of rivals Rangers at the top of the Scottish Premiership.